Design and Analysis of Algorithms MCQs - Timsort

1. What is the average number of comparisons used to heap sort a random permutation of N distinct items?
a) 2N log N-O(N)
b) 2N log N-O(N log N)
c) 2N log N-O(N log log N)
d) 2N log N-O(log N)

Answer: c
Explanation: According to a theorem, the average number of comparisons used to heap sort a random permutation of N distinct items is found to be 2N log N-O(N log log N).

2. Which of the following is Python’s standard sorting algorithm?
a) quick sort
b) introsort
c) merge sort
d) tim sort

Answer: d
Explanation: Tim sort has been python’s standard sorting algorithm since its version 2.3. It is an example of hybrid sorting algorithm which means it uses more than one sorting algorithm as a routine.

3. Which of the following sorting algorithm is a constituent of tim sort?
a) selection sort
b) quick sort
c) merge sort
d) heap sort

Answer: c
Explanation: Tim sort is a hybrid sorting algorithm which means it uses more than one sorting algorithm as a routine. It is derived from insertion sort and merge sort.

4. Tim sort begins sorting the given array by using which of the following sorting algorithm?
a) selection sort
b) quick sort
c) insertion sort
d) merge sort

Answer: c
Explanation: Tim sort begins sorting any given array by using insertion sort for each run. The array is divided into smaller parts for this purpose, each part having a size equal to value of run. Then these small parts called runs are merged in order to obtain sorted array.

5. Which of the following sorting algorithm is stable?
a) Tim sort
b) Introsort
c) Quick sort
d) Heap sort

Answer: a
Explanation: Out of the given options Tim sort is the only algorithm which is stable. As both constituents of Tim sort (I.e insertion sort and merge sort) are stable so Tim sort also becomes stable.

6. Which of the following sorting algorithm is not in-place?
a) insertion sort
b) tim sort
c) quick sort
d) intro sort

Answer: b
Explanation: Tim sort is not an in-place sorting algorithm as it requires auxiliary space. It is because it requires to merge sorted runs which requires a third array of the size equal to the sum of the two runs.

7. What is the best case time complexity of Tim sort?
a) O(n)
b) O(n log n)
c) O(n2)
d) O(log n)

Answer: a
Explanation: Best case time complexity of Tim sort occurs when the input array is already sorted. In such a case only one run will be required.

8. What is the worst case time complexity of Tim sort?
a) O(n)
b) O(n log n)
c) O(n2)
d) O(log n)

Answer: b
Explanation: Worst case time complexity of Tim sort is O(n log n). It is because the worst complexity of merge sort is O(n log n) and insertion sort is only applied for small arrays.

9. What is the average time complexity of Tim sort?
a) O(n)
b) O(n log n)
c) O(n2)
d) O(log n)

Answer: b
Explanation: Average time complexity of Tim sort remains to be O(n log n). It is the same as the average case complexity of merge sort.

10. What is the auxiliary space requirement of Tim sort?
a) O(n)
b) O(n log n)
c) O(n2)
d) O(log n)

Answer: a
Explanation: Tim sort is a hybrid of merge sort and insertion sort. It requires to merge sorted runs which require a third array of the size equal to the sum of the two runs. So in worst case the auxiliary space requirement will be O(n).



Design and Analysis of Algorithms

The Timsort Tango: An Algorithmic Ballroom


Imagine sorting algorithms as dancers in a grand ballroom. Timsort elegantly waltzes in, showcasing its prowess in the delicate art of sorting with finesse. This algorithm, born from the genius mind of Tim Peters, is a hybrid sorting algorithm derived from merge sort and insertion sort.

Design Delicacy: Timsort’s Unique Choreography


In the realm of sorting algorithms, Timsort is a standout performer. Its uniqueness lies in its ability to adapt to the characteristics of the input data. Small arrays? Insertion sort takes the lead. Larger ones? Merge sort swoops in for the grand performance.

The genius lies in its adaptive nature, gracefully adjusting its steps to the rhythm of the data. This makes Timsort a stellar choice for real-world scenarios where data comes in all shapes and sizes.

The Grand Finale: Timsort’s Impact


As our algorithmic ballroom dance nears its end, it's essential to appreciate Timsort's impact. Widely used in Python's sorting routines, this algorithm has become a staple in the world of computer science, showcasing the beauty of elegant design and efficient analysis.

In conclusion, as we bid adieu to the Timsort Tango, let's appreciate the symphony of algorithms and the dance they perform in the mesmerizing world of sorting.